Finite temperature phase diagram of a spin-polarized ultracold Fermi gas in a highly elongated harmonic trap

TL;DR

This paper maps out the finite temperature phase diagram of a spin-imbalanced ultracold Fermi gas in a highly elongated trap, revealing the survival of the FFLO phase at low temperatures and providing detailed thermodynamic properties relevant for experiments.

Contribution

It presents the first finite temperature phase diagram of a polarized Fermi gas in a trap, showing the temperature limits of the FFLO phase and analyzing thermodynamic properties.

Findings

FFLO phase persists below 0.1 Fermi temperature

Density profiles and equation of state are characterized

Results are relevant for ongoing experimental searches

Abstract

We investigate the finite temperature properties of an ultracold atomic Fermi gas with spin population imbalance in a highly elongated harmonic trap. Previous studies at zero temperature showed that the gas stays in an exotic spatially inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid state at the trap center; while moving to the edge, the system changes into either a non-polarized Bardeen-Cooper-Schriffer superfluid ($P<P_c$) or a fully polarized normal gas ($P>P_c$), depending on the smallness of the spin polarization $P$, relative to a critical value $P_c$. In this work, we show how these two phase-separation phases evolve with increasing temperature, and thereby construct a finite temperature phase diagram. For typical interactions, we find that the exotic FFLO phase survives below one-tenth of Fermi degeneracy temperature, which seems to be accessible in the current experiment. The density profile, equation of state, and specific heat of the polarized system have been calculated and discussed in detail. Our results are useful for the on-going experiment at Rice University on the search for FFLO states in quasi-one-dimensional polarized Fermi gases.